Theta-positive branching in varying environment
Probability
2025-11-18 v3
Abstract
Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough investigation of such processes within a continuous-time framework, assuming that the reproduction law of individuals adheres to a specific parametric form for the probability generating function. Our six clear-cut limit theorems support the notion of recognizing five distinct asymptotical regimes for branching in varying environments: supercritical, asymptotically degenerate, critical, strictly subcritical, and loosely subcritical.
Cite
@article{arxiv.2303.04230,
title = {Theta-positive branching in varying environment},
author = {Serik Sagitov and Alexey Lindo and Yerakhmet Zhumayev},
journal= {arXiv preprint arXiv:2303.04230},
year = {2025}
}